Robust and guaranteed output‐feedback force control of piezoelectric actuator under temperature variation and input constraints

Abstract

This paper addresses the control of manipulation force in a piezoelectric tube actuator (piezotube) subjected to temperature variation and input constrains. To handle this problem a robust output-feedback design is proposed using an interval state-space model, which permits consideration of the parameter uncertainties caused by temperature variation. The design method is robust in the sense that the eigenvalues of the interval system are designed to be clustered inside desired regions. For that, an algorithm based on Set Inversion Via Interval Analysis (SIVIA) combined with interval eigenvalues computation is proposed. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions of the feedback gain [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in the desired region, while at the same time ensuring the control inputs amplitude is bounded by specified saturation. The effectiveness of the control strategy is illustrated by experiments on a real piezotube of which the environmental temperature is varied. KEYWORDS input constraint, interval models, piezoelectric tube actuator, robust output-feedback, set inversion via interval analysis 1 INTRODUCTION Piezoelectric actuators, such as a piezoelectric tube and piezoelectric multimorph cantilever, are among the most used actuator in micro/nano-scales applications, particularly in micro/nano manipulation, Scanning Probe Microscopy (SPM), and Atomic Force Microscopy (AFM) due to their high speed (large bandwidth up to 1kHz), high precision (sub-nanometric), high resolution, and multi-degrees of freedom [1-6]. Unfortunately, they are characterized by nonlinearities (hysteresis, time varying parameters, creep, etc). They are also sensitive to the environment and especially to ambient temperature variation [7]. Actually, there are several sources that may cause this thermal variation during experimentation: the lamps used to illuminate the tasks at the microscale and related cameras, the heating of the surrounding devices (voltage amplifiers …), and all other natural sources. This temperature variation considerably impacts the approximated model of the actuator and induces the change in its dynamics and its steady-state behavior. Furthermore, in micro/nano manipulation, the manipulated object is usually so fragile that if the desired performance (overshoot and rapidity) is not sufficiently respected under

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